Question

What is the degree measure of an arc 4 πft? long in a circle of radius 10 ft.?

Answer 1

The length of an arc is given by the formula:

$\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \theta\colon\text{angular measure in degr}ee \\ r\colon\text{radius} \end{gathered}$

We are provided with the following;

$\begin{gathered} L_{\text{arc}}=4\pi\text{ ft} \\ r=10ft \end{gathered}$

Thus, we have:

$\begin{gathered} 4\pi=\frac{\theta}{360}\times2\pi\times10 \\ 4\pi\times360=\theta\times20\pi \\ \frac{4\pi\times360}{20\pi}=\theta \\ \theta=72^0 \end{gathered}$

Hence, the degree measure is 72 degrees